Add coconut milk and bring just to a boil, stirring and scraping up any browned bits from bottom of pan; reduce heat and simmer, stirring occasionally, until mixture is reduced by half, 10-15 minutes. Remove from heat and let cool.

Transfer coconut milk mixture to a blender. Add cilantro, lime juice, brown sugar, and 2 tablespoons water and blend until smooth. With motor running, drizzle in remaining 2 tablespoons oil and blend until creamy. Season curry sauce with salt and pepper, return to pan, and cover to keep warm.